A canon of mass `M` is mounted on an east west frictionless railway track. The barrel of cannon faces the north east direction at an angle of `45^(@)` with the vertical. The canon fires a shot of mass `M` with a speed `V` relative to the barrel.

Options

A. The recoil speed of the cannon will be `V//4`
B. The speed of the shot as seen from the ground will be `(sqrt(13))/(4)V`.
C. The momentum of the shot `+`canon system will remain conserved along the east west line.
D. The momentum of the shot plus canon system will remain conserved along the North South line.

Explanation

Conserving momentum along the east west line
`M(v cos^(2)45-v_(0))=Mv_(0)`
`rArr 2MV_(0)=MV cos^(2)45^(@)`
`rArr v_(0)=V//4`
Vertical speed `=(v)/(sqrt(2))`
North speed `=v cos^(2)45^(@)=(v)/(2)`
East speed `=(V)/(2)-(V)/(4)=(V)/(4)`
`rArr` Speed from ground `=vsqrt((1)/(2)+(1)/(4)+(1)/(16))=vsqrt((13)/(16))`